What is the integral of (x^2)/(e^{2x)} ?

The integral of (x^2)/(e^{2x)} is -1/2 e^{-2x}x^2+1/4 (-2e^{-2x}x-e^{-2x})+C

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integral of (x^2)/(e^{2x)}

\int \frac{x ^{2}}{e ^{2 x}} d x

- \frac{1}{2} e^{- 2 x} x^{2} + \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}) + C

Solution steps

\int \frac{x ^{2}}{e ^{2 x}} d x

Apply Integration By Parts

: - \frac{1}{2} e^{- 2 x} x^{2} - \int - e^{- 2 x} x d x

= - \frac{1}{2} e^{- 2 x} x^{2} - \int - e^{- 2 x} x d x

\int - e^{- 2 x} x d x = - \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x})

= - \frac{1}{2} e^{- 2 x} x^{2} - (- \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}))

Simplify

= - \frac{1}{2} e^{- 2 x} x^{2} + \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x})

Add a constant to the solution

= - \frac{1}{2} e^{- 2 x} x^{2} + \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}) + C

\frac{d}{d θ} (7 sin (θ))

- 2 x sin (x^{2})

\frac{d}{d x} ((sin (x))^{3})

\frac{1}{4} y^{^{''}} + 4 y = tan (4 t) - \frac{1}{2} e^{3 t}

x \to 0 lim (\frac{1 1 ^{x} - 1 0 ^{x}}{x})

What is the integral of (x^2)/(e^{2x)} ?
The integral of (x^2)/(e^{2x)} is -1/2 e^{-2x}x^2+1/4 (-2e^{-2x}x-e^{-2x})+C